This invention relates to microelectromechanical systems and/or nanoelectromechanical systems (collectively hereinafter “microelectromechanical systems”) and techniques for fabricating microelectromechanical systems; and more particularly, in one aspect, for fabricating, manufacturing, providing and/or controlling microelectromechanical resonators having mechanical structures that include integrated heating and/or temperature sensing elements; and in another aspect for fabricating, manufacturing, providing and/or controlling microelectromechanical resonators having mechanical structures that are encapsulated using thin film or wafer level encapsulation techniques in a chamber, and include heating and/or temperature sensing elements disposed in the chamber, on the chamber and/or integrated within the mechanical structures.
Many conventional micromechanical structures are based on the reaction (for example, oscillation, deflection or torsion) of a beam structure to an applied force. Such beam structures are fabricated from monocrystalline or polycrystalline semiconductors, such as silicon. These materials have excellent mechanical strength and a high intrinsic quality factor. Furthermore, the formation and processing of silicon-based materials are well-developed fields of endeavor.
For example, using polycrystalline silicon, one may design micromechanical resonators having great flexibility in geometry. Such resonators typically rely upon the bending beam and lateral oscillating beam structures. Notably, the beam structures are often rectangular in shape and/or cross section.
The mechanical stiffness, kM, of a beam, as calculated with respect to the oscillation direction parallel to the width of the beam (w), is proportional to its Young's modulus (E) and certain measures of its geometry, including for a beam with a rectangular cross section, length (L) and height (h).
                              k          M                ≈                              E            ·            h            ·                          w              3                                            L            3                                              EQUATION        ⁢                                  ⁢        1            
As is well understood, the Young's modulus for most materials of interest changes with temperature according to known thermal coefficients (αE). For example, the Young's modulus of polysilicon has a thermal coefficient of approximately 30 ppm/K°. Furthermore, the geometry of a beam structure also changes with temperature, generally expanding with increasing in temperature. Again, as an example, polysilicon has a thermal expansion coefficient (αexp) of approximately 2.5 ppm/K°.
For some beam designs and related modeling purposes (given a material with an isotropic thermal coefficient), the effect of thermal expansion on the width of the beam is essentially offset by the effect of thermal expansion on the length of the beam, thus resulting in a remaining linear effect on the height of the beam.
Setting aside electrostatic forces, the resonance frequency (f) of a beam may thus be defined under these assumptions by the equation:
                    f        ≈                              1                          2              ·              π                                ·                                                    k                M                                            m                eff                                                                        EQUATION        ⁢                                  ⁢        2            
where meff is the effective mass of the beam, which is constant over temperature.
Given the critical nature of a beam's resonance frequency to the overall performance of the resonator, it should remain relatively stable over a range of operating temperatures. In view of the relationship set forth in EQUATION 2, the frequency of the resonator will remain constant if the mechanical stiffness remains constant. This, however, will not normally be the case as thermally induced changes to the Young's modulus tend to change the mechanical stiffness of the beam.
There have been many attempts to address the issue of resonant beam frequency stabilization in the presence of a changing operating temperature. See, for example, Wan-Thai Hsu, “Stiffness-Compensated Temperature Insensitive Micromechanical Resonators”, MEMS 2002 (0-7803-7185-2/02, 2002 IEEE) and Wan-Thai Hsu et al., “Mechanically Temperature-Compensated Flexural-Mode Micromechanical Resonators”, IEDM 00-399 (0-7803-6438-4/00, 2000 IEEE) (hereinafter, “the Mechanically Temperature-Compensated Resonators reference”). Such approaches focus on compensating changes in vertical oscillation, prescribe the remedial use of gold or similar materials that are incompatible with CMOS integration, and/or propose techniques that employ significant power consumption.
For example, in the Mechanically Temperature-Compensated Resonators reference, it is proposed to employ an undulating heating element disposed beneath the entire micromechanical resonator. Such a configuration, and, in particular, the heating element, may, among other things, consume a significant amount of power because of the large heat loss to the surroundings/environment. In addition, such a configuration employs unfocused or non-specific heating of the entire micromechanical resonator. (See, FIG. 1 of the Mechanically Temperature-Compensated Resonators reference).
Thus, there is a need for a micromechanical resonator whose output frequency is relatively stable over an operating range of temperatures and that overcomes one, some or all of the shortcomings of conventional resonators. There is a need for a micromechanical resonator that compensates for, and/or addresses, minimizes and/or eliminates the adverse affects of variations in operating temperature by employing focused or specific heating of critical aspects of micromechanical resonator.
Moreover, there is a need for an efficient compensation technique for frequency stability of micromechanical resonators over an operating temperature range that overcome one, some or all of the shortcomings of conventional resonators. Notably, it may be advantageous if such a technique does not rely on the incorporation of materials that are incompatible with CMOS integration.